Maggie is rock climbing. After reaching the summit she descends $14$ feet in $2 \frac{1}{3}$ minutes. If she continues at this rate,where will Maggie be in the relation to the summit after $8$ minutes?

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Q. Maggie is rock climbing. After reaching the summit she descends

14

feet in

2 \frac{1}{3}

minutes. If she continues at this rate,where will Maggie be in the relation to the summit after

8

minutes?

Determine Rate of Descent: First, we need to determine Maggie's rate of descent in feet per minute. She descends $14$ feet in $2 \frac{1}{3}$ minutes. To find the rate, we divide the distance by the time.
Convert to Improper Fraction: Convert $2\frac{1}{3}$ minutes to an improper fraction to make the division easier. $2\frac{1}{3}$ minutes is the same as $\frac{7}{3}$ minutes.
Calculate Rate of Descent: Now, divide $14$ feet by $\frac{7}{3}$ minutes to find the rate of descent in feet per minute. To divide by a fraction, multiply by its reciprocal. So, we multiply $14$ feet by $\frac{3}{7}$ .
Simplify Rate: The calculation for the rate is $14 \text{ feet} \times \left(\frac{3}{7}\right) = \frac{42}{7} \text{ feet per minute}.$
Calculate Distance: Simplify $42/7$ to get the rate of descent, which is $6$ feet per minute.
Calculate Final Position: Now that we know Maggie descends at a rate of $6$ feet per minute, we can calculate how far she will descend in $8$ minutes. Multiply the rate of descent by the time to get the distance.
Calculate Final Position: Now that we know Maggie descends at a rate of $6$ feet per minute, we can calculate how far she will descend in $8$ minutes. Multiply the rate of descent by the time to get the distance.The calculation for the distance is $6$ feet/minute $\times$ $8$ minutes $= 48$ feet.
Calculate Final Position: Now that we know Maggie descends at a rate of $6$ feet per minute, we can calculate how far she will descend in $8$ minutes. Multiply the rate of descent by the time to get the distance.The calculation for the distance is $6$ feet/minute $\times$ $8$ minutes $= 48$ feet.Maggie will be $48$ feet below the summit after descending for $8$ minutes at her current rate.